For a detailed discussion of this, I recommend A History of New Testament Lexicography by John A. L. Lee. It specifically explores how translators have relied heavily on lexicons, which in turn rely heavily on earlier translations and other lexicons.
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fumanchuAug 6 '12 at 15:17

1 Answer
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Can do either, obviously. If they edit an existing translation, this is called a "rescension" (The Living Bible was one, a paraphrase of the KJV). However, most of the time, they use Hebrew, Greek, and Aramaic text. As an example, The New Living Translation does this. But they don't stop with just one manuscript. They compare different manuscripts of a text to determine what was originally written. This is called "textual criticism".

Even when going back to the original languages, the translators will look at already known and established translations to determine how other scholars have handled the tricky parts of the grammar.